The generalized 2-connectivity is exactly the classical connectivity. Over the past few years, research on the generalized connectivity has received meaningful progress. Li et al. [1]} derived that it is NP-complete for a general graph \(G\)  to decide whether there are \(l\)  internally disjoint trees connecting \(S\) , where \(l\)  is a fixed integer and \(S\subseteq V(G)\) . Authors in [2]}, [3]} investigated the upper and lower bounds of the generalized connectivity of a general graph \(G\) .
